Year: 2022
Author: Yuling Guo, Jianguo Huang
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 3 : pp. 662–678
Abstract
This paper develops a posteriori error bound for a space-time finite element method for the linear wave equation. The standard $P_l$ conforming element is used for the spatial discretization and a $P_2$-CDG method is applied for the time discretization. The essential ingredients in the a posteriori error analysis are the twice time reconstruction functions and the $C^1(J)$-smooth elliptic reconstruction, which lead to reliable a posteriori error bound in view of the energy method. As an outcome, a time adaptive algorithm is proposed with the error equidistribution strategy. Numerical experiments are reported to illustrate the performance of the a posteriori error bound and the validity of the adaptive algorithm.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2022-0012
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 3 : pp. 662–678
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: $P_2$-CDG wave equations a posteriori error estimate.